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Vlad [161]
2 years ago
5

If you have a cube with a side length of ¼, how many cubes can fit into your rectangular prism? Explain.

Mathematics
1 answer:
sergey [27]2 years ago
6 0

Answer:

Step-by-step explanation:

No of cubes that can fit into rectangular prism =  <u> Volume of rectangular prism</u>

                                                                                   Volume of cube

Find the volume of rectangular prism and divide that by the volume of cube

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i have been trying to solve this compound and double angle question please help me find the answer to these question guys​
natali 33 [55]

Answer:

These type of questions are super tricky b/c you have to remember all the different versions of the identities, and then they put the question in some odd form,  I feel like this should land math professors in jail , for dishonesty , b/c it's really a form of "how tricky can I make a question and still have a way to solve it"   anyway,

Step-by-step explanation:

a)

next the question asks   1-cos 2A   and this is total abuse of notation.   the way this should be written is   1- cos( 2A)  so we know that the A is part of the cosine functions input... btw.. in any computer program,  it would never ever let you get away with that top form of the expression.  :/   anyway... I keep ranting.. huh... sorry  :P

1-cos(2A) is an odd form of the identity  1/2(1-cos(2A) = sin^{2}(A)  the 1/2 is missing but we can add that pretty easy, we just have to remember to take it out too. I usually forget to do that. and my professor marks me off completely,  totally wrong, but I just miss one small thing  :/  anyway....

our 1-cos(2A) needs the 1/2 added to it.  or if we move that 1/2 to the other side it looks like  2*sin^{2}(A)  = 1-cos(2A)  and this is that "odd" from of the identity that I was talking about.  

next let's deal with sin(2A)  it has an identity of  2 sin(A)cos(A) which is really nice for us b/c it will cancel out the 2 in then numerator for us, nice !

now our fraction looks like  [2* sin^{2}(A)] / 2 sin(A)cos(A)

so cancel out one of the sines

2*sin(A) / 2 cos(A)

cancel the 2s

Sin(A) / Cos(A) = Tan(A)

nice  it worked out  :P

b)

by the above that we just worked out, then

Tan(15) = Sin(15) / Cos(15)

I had to look up what sin of 15 is b/c it's not one of those special angles but it does have an exact form of

Sin(15) = (√3 - 1) / 2√2

Cos(A) = (√3 + 1) / 2√2

you can use rule of Cos(A-B) = Cos(A)Cos(B)+Sin(A)Sin(B) to get the above and a similar rule for Sin(A-B)

back to our problem,  the 2√2 will cancel out

then we have

Tan(15) =  (√3 - 1) /(√3 + 1)

in the form that is above that's exact, the roots could be approximated but i'll just leave that in the form that is exact.  Most math professors like that form.  

 

4 0
2 years ago
The low temperature on Monday was 5 F. During the day, the temperature rose 20. What was the high temperature on Monday?
maria [59]

Answer:

the temp rose up 15 dgrs

Step-by-step explanation:

7 0
3 years ago
Distributive property to 5 (y-8)
bazaltina [42]
5y-40
5 multiply y and 5 multiply -8
hope this helps !
8 0
2 years ago
Linda drove 638 miles in 11 hours. at the same rate, how many miles would she drive in 9 hours?
Igoryamba
638 divided by 11= 58. 58x9=522
6 0
2 years ago
What is the vertex of the quadratic function f(x)=(x-8)(x-2)
Mrac [35]

So firstly, foil (x-8)(x-2): f(x)=x^2-2x-8x+16\\ f(x)=x^2-10x+16

Next, remember that the vertex lies on the axis of symmetry, and the equation to find the axis of symmetry is x=\frac{-b}{2a} (a = x^2 coefficient, b = x coefficient). Solve for the axis of symmetry as such:

x=\frac{10}{2*1}=\frac{10}{2}=5

So now that we know that the axis of symmetry is x = 5, we also know that's the vertex's x-coordinate (since the vertex falls on the axis of symmetry). Now plug in 5 for x in the original equation to solve for f(5):

f(5)=5^2-10(5)+16\\ f(5)=25-50+16\\ f(5)=-9

So putting it together, the vertex of this equation is (5,-9).

4 0
2 years ago
Read 2 more answers
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